In 2001, the right-hander was 6-3 with a 3.38 ERA for the Pulaski Rangers with 83 K in 69 1/3 IP. He tied for the Appalachian League in victories. He did not pitch in 2002 due to injury. Returning to action in 2003 with the Clinton Lumber Kings, Omar was 3-3 with a save and a 2.39 ERA. By 2004, he was in high-A with the Stockton Ports, going 4-5 with six saves and a 2.45 ERA. In the 2005 Dominican League, he tossed 12 innings for the Azucareros del Este and did not allow an earned run. That year, his career skidded to a halt. When he and other players from the Dominican Republic went to get their work visas, it was discovered that a surprising number had married in the off-season. It was later revealed that the players had been paid to marry women so that they could get into the US. Beltré was turned down for his visa, as were the others involved. He and the other players involved were handed a five-year exclusion from the United States for their role in the ring, a sentence which ended most of the participants' baseball career, but Beltre carried on, as did Alexi Ogando.

In 2005, Beltre thus spent the year with the DSL Rangers, going 5-4 with a 1.62 ERA and 94 K in 72 1/3 IP, allowing 51 hits. Texas added him to their 40-man roster that November. He had a 3.18 ERA for the Azucareros in the winter season. Beltré tried getting his visa again that spring, but failed. He was dominant with the DSL Rangers, going 2-3 with a save but with a 1.07 ERA, 42 hits and 80 K in 66 innings. He was 5th in the Dominican Summer League in ERA.

During 2007, the veteran hurler had a 4-3, 2.03 record for the Azucareros and allowed a .187 average. Texas tried getting a special visa for him that year but failed. He returned to the DSL Rangers for a third season and was 2-0 with a 1.17 ERA and 38 K in 30 2/3 IP. He also pitched for the Dominican Republic in the 2007 Pan American Games, allowing 3 runs (2 earned) and fanning 5 in 4 2/3 IP in a loss to Team USA and Tyson Ross.

That winter, he fell to 2-2, 4.35 for the Azucareros. He did pitch in the 2008 Caribbean Series, though. Still unable to enter the USA, Beltré allowed 3 unearned runs in 7 1/3 innings for the 2009 DSL Rangers 2.

Beltré's five-year exclusion from the United States for his participation in the human trafficking scheme ended in 2010, and he jumped all the way to AAA to start the season, pitching for the Oklahoma City RedHawks of the Pacific Coast League. He went 0-5 over his first 15 games, but with an excellent 2.39 ERA and 44 strikeouts in 37⅔ innings. He was called up by the Rangers in late June and made his major league debut as a starter facing the Los Angeles Angels on June 30, 2010. He gave up a home run to the first batter he faced in the majors - Erick Aybar - and was removed after 4 innings, having given up 3 runs on 5 hits and 4 walks. He did strike out 6 batters, though, showing some lively stuff, and the Rangers won the game, 6-4, to set a franchise record with 21 wins in the month of June.